Load MASS library, as we need to work on Boston dataset.

library(MASS)
#Boston
names(Boston)
##  [1] "crim"    "zn"      "indus"   "chas"    "nox"     "rm"      "age"    
##  [8] "dis"     "rad"     "tax"     "ptratio" "black"   "lstat"   "medv"

We will create a simple single linear regression model with Boston library’s lstat as predictor and medv as response.

#lm.fit=lm(medv~lstat, data=Boston)
attach(Boston)
lm.fit = lm(medv~lstat)
lm.fit
## 
## Call:
## lm(formula = medv ~ lstat)
## 
## Coefficients:
## (Intercept)        lstat  
##       34.55        -0.95
summary(lm.fit)
## 
## Call:
## lm(formula = medv ~ lstat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.168  -3.990  -1.318   2.034  24.500 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 34.55384    0.56263   61.41   <2e-16 ***
## lstat       -0.95005    0.03873  -24.53   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.216 on 504 degrees of freedom
## Multiple R-squared:  0.5441, Adjusted R-squared:  0.5432 
## F-statistic: 601.6 on 1 and 504 DF,  p-value: < 2.2e-16
anova(lm.fit)
## Analysis of Variance Table
## 
## Response: medv
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## lstat       1  23244 23243.9  601.62 < 2.2e-16 ***
## Residuals 504  19472    38.6                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(lstat, medv)
abline(h=mean(medv))
abline(lm.fit, col="blue")

names(lm.fit)
##  [1] "coefficients"  "residuals"     "effects"       "rank"         
##  [5] "fitted.values" "assign"        "qr"            "df.residual"  
##  [9] "xlevels"       "call"          "terms"         "model"
confint(lm.fit)
##                 2.5 %     97.5 %
## (Intercept) 33.448457 35.6592247
## lstat       -1.026148 -0.8739505
predict(lm.fit ,data.frame(lstat=c(5 ,10 ,15)),interval ="confidence")
##        fit      lwr      upr
## 1 29.80359 29.00741 30.59978
## 2 25.05335 24.47413 25.63256
## 3 20.30310 19.73159 20.87461

Residual plots:

plot(lm.fit)

Now that we have gone through a single linear regression model (with one predictor), we will create a multiple linear regression model with all thirteen predictors:

mul.lm.fit = lm(medv ~ ., data = Boston)
summary(mul.lm.fit)
## 
## Call:
## lm(formula = medv ~ ., data = Boston)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.595  -2.730  -0.518   1.777  26.199 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.646e+01  5.103e+00   7.144 3.28e-12 ***
## crim        -1.080e-01  3.286e-02  -3.287 0.001087 ** 
## zn           4.642e-02  1.373e-02   3.382 0.000778 ***
## indus        2.056e-02  6.150e-02   0.334 0.738288    
## chas         2.687e+00  8.616e-01   3.118 0.001925 ** 
## nox         -1.777e+01  3.820e+00  -4.651 4.25e-06 ***
## rm           3.810e+00  4.179e-01   9.116  < 2e-16 ***
## age          6.922e-04  1.321e-02   0.052 0.958229    
## dis         -1.476e+00  1.995e-01  -7.398 6.01e-13 ***
## rad          3.060e-01  6.635e-02   4.613 5.07e-06 ***
## tax         -1.233e-02  3.760e-03  -3.280 0.001112 ** 
## ptratio     -9.527e-01  1.308e-01  -7.283 1.31e-12 ***
## black        9.312e-03  2.686e-03   3.467 0.000573 ***
## lstat       -5.248e-01  5.072e-02 -10.347  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.745 on 492 degrees of freedom
## Multiple R-squared:  0.7406, Adjusted R-squared:  0.7338 
## F-statistic: 108.1 on 13 and 492 DF,  p-value: < 2.2e-16
plot(mul.lm.fit)

Multiple linear regression without a predictor, for example: age.

mul.lm.fit.without.age = update(mul.lm.fit, ~ . -age)
summary(mul.lm.fit.without.age)
## 
## Call:
## lm(formula = medv ~ crim + zn + indus + chas + nox + rm + dis + 
##     rad + tax + ptratio + black + lstat, data = Boston)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.6054  -2.7313  -0.5188   1.7601  26.2243 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  36.436927   5.080119   7.172 2.72e-12 ***
## crim         -0.108006   0.032832  -3.290 0.001075 ** 
## zn            0.046334   0.013613   3.404 0.000719 ***
## indus         0.020562   0.061433   0.335 0.737989    
## chas          2.689026   0.859598   3.128 0.001863 ** 
## nox         -17.713540   3.679308  -4.814 1.97e-06 ***
## rm            3.814394   0.408480   9.338  < 2e-16 ***
## dis          -1.478612   0.190611  -7.757 5.03e-14 ***
## rad           0.305786   0.066089   4.627 4.75e-06 ***
## tax          -0.012329   0.003755  -3.283 0.001099 ** 
## ptratio      -0.952211   0.130294  -7.308 1.10e-12 ***
## black         0.009321   0.002678   3.481 0.000544 ***
## lstat        -0.523852   0.047625 -10.999  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.74 on 493 degrees of freedom
## Multiple R-squared:  0.7406, Adjusted R-squared:  0.7343 
## F-statistic: 117.3 on 12 and 493 DF,  p-value: < 2.2e-16

Multiple linear regression with interaction terms

mul.lm.fit.interact.age = lm(medv ~ lstat * age, data = Boston)
summary(mul.lm.fit.interact.age)
## 
## Call:
## lm(formula = medv ~ lstat * age, data = Boston)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.806  -4.045  -1.333   2.085  27.552 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 36.0885359  1.4698355  24.553  < 2e-16 ***
## lstat       -1.3921168  0.1674555  -8.313 8.78e-16 ***
## age         -0.0007209  0.0198792  -0.036   0.9711    
## lstat:age    0.0041560  0.0018518   2.244   0.0252 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.149 on 502 degrees of freedom
## Multiple R-squared:  0.5557, Adjusted R-squared:  0.5531 
## F-statistic: 209.3 on 3 and 502 DF,  p-value: < 2.2e-16

Non-linear Transformations of the Predictors with single predictor:

lm.fit.non.linear = lm(medv ~ lstat + I(lstat^2), data = Boston)
summary(lm.fit.non.linear)
## 
## Call:
## lm(formula = medv ~ lstat + I(lstat^2), data = Boston)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.2834  -3.8313  -0.5295   2.3095  25.4148 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 42.862007   0.872084   49.15   <2e-16 ***
## lstat       -2.332821   0.123803  -18.84   <2e-16 ***
## I(lstat^2)   0.043547   0.003745   11.63   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.524 on 503 degrees of freedom
## Multiple R-squared:  0.6407, Adjusted R-squared:  0.6393 
## F-statistic: 448.5 on 2 and 503 DF,  p-value: < 2.2e-16
plot(lm.fit.non.linear)

# attach(Boston)
# plot(lstat, medv)
# abline(lm.fit.non.linear, col="blue")
anova(lm.fit, lm.fit.non.linear)
## Analysis of Variance Table
## 
## Model 1: medv ~ lstat
## Model 2: medv ~ lstat + I(lstat^2)
##   Res.Df   RSS Df Sum of Sq     F    Pr(>F)    
## 1    504 19472                                 
## 2    503 15347  1    4125.1 135.2 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Polynomial fit for linear regression:

lm.fit.non.linear.degree5 = lm(medv ~ poly(lstat, 5), data = Boston)
summary(lm.fit.non.linear.degree5)
## 
## Call:
## lm(formula = medv ~ poly(lstat, 5), data = Boston)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.5433  -3.1039  -0.7052   2.0844  27.1153 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       22.5328     0.2318  97.197  < 2e-16 ***
## poly(lstat, 5)1 -152.4595     5.2148 -29.236  < 2e-16 ***
## poly(lstat, 5)2   64.2272     5.2148  12.316  < 2e-16 ***
## poly(lstat, 5)3  -27.0511     5.2148  -5.187 3.10e-07 ***
## poly(lstat, 5)4   25.4517     5.2148   4.881 1.42e-06 ***
## poly(lstat, 5)5  -19.2524     5.2148  -3.692 0.000247 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.215 on 500 degrees of freedom
## Multiple R-squared:  0.6817, Adjusted R-squared:  0.6785 
## F-statistic: 214.2 on 5 and 500 DF,  p-value: < 2.2e-16
plot(lm.fit.non.linear.degree5)

======================CARSEATS DATASET FOR QUALITATIVE PREDICTORS========================

library(ISLR)
names(Carseats)
##  [1] "Sales"       "CompPrice"   "Income"      "Advertising" "Population" 
##  [6] "Price"       "ShelveLoc"   "Age"         "Education"   "Urban"      
## [11] "US"
Carseats
##     Sales CompPrice Income Advertising Population Price ShelveLoc Age
## 1    9.50       138     73          11        276   120       Bad  42
## 2   11.22       111     48          16        260    83      Good  65
## 3   10.06       113     35          10        269    80    Medium  59
## 4    7.40       117    100           4        466    97    Medium  55
## 5    4.15       141     64           3        340   128       Bad  38
## 6   10.81       124    113          13        501    72       Bad  78
## 7    6.63       115    105           0         45   108    Medium  71
## 8   11.85       136     81          15        425   120      Good  67
## 9    6.54       132    110           0        108   124    Medium  76
## 10   4.69       132    113           0        131   124    Medium  76
## 11   9.01       121     78           9        150   100       Bad  26
## 12  11.96       117     94           4        503    94      Good  50
## 13   3.98       122     35           2        393   136    Medium  62
## 14  10.96       115     28          11         29    86      Good  53
## 15  11.17       107    117          11        148   118      Good  52
## 16   8.71       149     95           5        400   144    Medium  76
## 17   7.58       118     32           0        284   110      Good  63
## 18  12.29       147     74          13        251   131      Good  52
## 19  13.91       110    110           0        408    68      Good  46
## 20   8.73       129     76          16         58   121    Medium  69
## 21   6.41       125     90           2        367   131    Medium  35
## 22  12.13       134     29          12        239   109      Good  62
## 23   5.08       128     46           6        497   138    Medium  42
## 24   5.87       121     31           0        292   109    Medium  79
## 25  10.14       145    119          16        294   113       Bad  42
## 26  14.90       139     32           0        176    82      Good  54
## 27   8.33       107    115          11        496   131      Good  50
## 28   5.27        98    118           0         19   107    Medium  64
## 29   2.99       103     74           0        359    97       Bad  55
## 30   7.81       104     99          15        226   102       Bad  58
## 31  13.55       125     94           0        447    89      Good  30
## 32   8.25       136     58          16        241   131    Medium  44
## 33   6.20       107     32          12        236   137      Good  64
## 34   8.77       114     38          13        317   128      Good  50
## 35   2.67       115     54           0        406   128    Medium  42
## 36  11.07       131     84          11         29    96    Medium  44
## 37   8.89       122     76           0        270   100      Good  60
## 38   4.95       121     41           5        412   110    Medium  54
## 39   6.59       109     73           0        454   102    Medium  65
## 40   3.24       130     60           0        144   138       Bad  38
## 41   2.07       119     98           0         18   126       Bad  73
## 42   7.96       157     53           0        403   124       Bad  58
## 43  10.43        77     69           0         25    24    Medium  50
## 44   4.12       123     42          11         16   134    Medium  59
## 45   4.16        85     79           6        325    95    Medium  69
## 46   4.56       141     63           0        168   135       Bad  44
## 47  12.44       127     90          14         16    70    Medium  48
## 48   4.38       126     98           0        173   108       Bad  55
## 49   3.91       116     52           0        349    98       Bad  69
## 50  10.61       157     93           0         51   149      Good  32
## 51   1.42        99     32          18        341   108       Bad  80
## 52   4.42       121     90           0        150   108       Bad  75
## 53   7.91       153     40           3        112   129       Bad  39
## 54   6.92       109     64          13         39   119    Medium  61
## 55   4.90       134    103          13         25   144    Medium  76
## 56   6.85       143     81           5         60   154    Medium  61
## 57  11.91       133     82           0         54    84    Medium  50
## 58   0.91        93     91           0         22   117       Bad  75
## 59   5.42       103     93          15        188   103       Bad  74
## 60   5.21       118     71           4        148   114    Medium  80
## 61   8.32       122    102          19        469   123       Bad  29
## 62   7.32       105     32           0        358   107    Medium  26
## 63   1.82       139     45           0        146   133       Bad  77
## 64   8.47       119     88          10        170   101    Medium  61
## 65   7.80       100     67          12        184   104    Medium  32
## 66   4.90       122     26           0        197   128    Medium  55
## 67   8.85       127     92           0        508    91    Medium  56
## 68   9.01       126     61          14        152   115    Medium  47
## 69  13.39       149     69          20        366   134      Good  60
## 70   7.99       127     59           0        339    99    Medium  65
## 71   9.46        89     81          15        237    99      Good  74
## 72   6.50       148     51          16        148   150    Medium  58
## 73   5.52       115     45           0        432   116    Medium  25
## 74  12.61       118     90          10         54   104      Good  31
## 75   6.20       150     68           5        125   136    Medium  64
## 76   8.55        88    111          23        480    92       Bad  36
## 77  10.64       102     87          10        346    70    Medium  64
## 78   7.70       118     71          12         44    89    Medium  67
## 79   4.43       134     48           1        139   145    Medium  65
## 80   9.14       134     67           0        286    90       Bad  41
## 81   8.01       113    100          16        353    79       Bad  68
## 82   7.52       116     72           0        237   128      Good  70
## 83  11.62       151     83           4        325   139      Good  28
## 84   4.42       109     36           7        468    94       Bad  56
## 85   2.23       111     25           0         52   121       Bad  43
## 86   8.47       125    103           0        304   112    Medium  49
## 87   8.70       150     84           9        432   134    Medium  64
## 88  11.70       131     67           7        272   126      Good  54
## 89   6.56       117     42           7        144   111    Medium  62
## 90   7.95       128     66           3        493   119    Medium  45
## 91   5.33       115     22           0        491   103    Medium  64
## 92   4.81        97     46          11        267   107    Medium  80
## 93   4.53       114    113           0         97   125    Medium  29
## 94   8.86       145     30           0         67   104    Medium  55
## 95   8.39       115     97           5        134    84       Bad  55
## 96   5.58       134     25          10        237   148    Medium  59
## 97   9.48       147     42          10        407   132      Good  73
## 98   7.45       161     82           5        287   129       Bad  33
## 99  12.49       122     77          24        382   127      Good  36
## 100  4.88       121     47           3        220   107       Bad  56
## 101  4.11       113     69          11         94   106    Medium  76
## 102  6.20       128     93           0         89   118    Medium  34
## 103  5.30       113     22           0         57    97    Medium  65
## 104  5.07       123     91           0        334    96       Bad  78
## 105  4.62       121     96           0        472   138    Medium  51
## 106  5.55       104    100           8        398    97    Medium  61
## 107  0.16       102     33           0        217   139    Medium  70
## 108  8.55       134    107           0        104   108    Medium  60
## 109  3.47       107     79           2        488   103       Bad  65
## 110  8.98       115     65           0        217    90    Medium  60
## 111  9.00       128     62           7        125   116    Medium  43
## 112  6.62       132    118          12        272   151    Medium  43
## 113  6.67       116     99           5        298   125      Good  62
## 114  6.01       131     29          11        335   127       Bad  33
## 115  9.31       122     87           9         17   106    Medium  65
## 116  8.54       139     35           0         95   129    Medium  42
## 117  5.08       135     75           0        202   128    Medium  80
## 118  8.80       145     53           0        507   119    Medium  41
## 119  7.57       112     88           2        243    99    Medium  62
## 120  7.37       130     94           8        137   128    Medium  64
## 121  6.87       128    105          11        249   131    Medium  63
## 122 11.67       125     89          10        380    87       Bad  28
## 123  6.88       119    100           5         45   108    Medium  75
## 124  8.19       127    103           0        125   155      Good  29
## 125  8.87       131    113           0        181   120      Good  63
## 126  9.34        89     78           0        181    49    Medium  43
## 127 11.27       153     68           2         60   133      Good  59
## 128  6.52       125     48           3        192   116    Medium  51
## 129  4.96       133    100           3        350   126       Bad  55
## 130  4.47       143    120           7        279   147       Bad  40
## 131  8.41        94     84          13        497    77    Medium  51
## 132  6.50       108     69           3        208    94    Medium  77
## 133  9.54       125     87           9        232   136      Good  72
## 134  7.62       132     98           2        265    97       Bad  62
## 135  3.67       132     31           0        327   131    Medium  76
## 136  6.44        96     94          14        384   120    Medium  36
## 137  5.17       131     75           0         10   120       Bad  31
## 138  6.52       128     42           0        436   118    Medium  80
## 139 10.27       125    103          12        371   109    Medium  44
## 140 12.30       146     62          10        310    94    Medium  30
## 141  6.03       133     60          10        277   129    Medium  45
## 142  6.53       140     42           0        331   131       Bad  28
## 143  7.44       124     84           0        300   104    Medium  77
## 144  0.53       122     88           7         36   159       Bad  28
## 145  9.09       132     68           0        264   123      Good  34
## 146  8.77       144     63          11         27   117    Medium  47
## 147  3.90       114     83           0        412   131       Bad  39
## 148 10.51       140     54           9        402   119      Good  41
## 149  7.56       110    119           0        384    97    Medium  72
## 150 11.48       121    120          13        140    87    Medium  56
## 151 10.49       122     84           8        176   114      Good  57
## 152 10.77       111     58          17        407   103      Good  75
## 153  7.64       128     78           0        341   128      Good  45
## 154  5.93       150     36           7        488   150    Medium  25
## 155  6.89       129     69          10        289   110    Medium  50
## 156  7.71        98     72           0         59    69    Medium  65
## 157  7.49       146     34           0        220   157      Good  51
## 158 10.21       121     58           8        249    90    Medium  48
## 159 12.53       142     90           1        189   112      Good  39
## 160  9.32       119     60           0        372    70       Bad  30
## 161  4.67       111     28           0        486   111    Medium  29
## 162  2.93       143     21           5         81   160    Medium  67
## 163  3.63       122     74           0        424   149    Medium  51
## 164  5.68       130     64           0         40   106       Bad  39
## 165  8.22       148     64           0         58   141    Medium  27
## 166  0.37       147     58           7        100   191       Bad  27
## 167  6.71       119     67          17        151   137    Medium  55
## 168  6.71       106     73           0        216    93    Medium  60
## 169  7.30       129     89           0        425   117    Medium  45
## 170 11.48       104     41          15        492    77      Good  73
## 171  8.01       128     39          12        356   118    Medium  71
## 172 12.49        93    106          12        416    55    Medium  75
## 173  9.03       104    102          13        123   110      Good  35
## 174  6.38       135     91           5        207   128    Medium  66
## 175  0.00       139     24           0        358   185    Medium  79
## 176  7.54       115     89           0         38   122    Medium  25
## 177  5.61       138    107           9        480   154    Medium  47
## 178 10.48       138     72           0        148    94    Medium  27
## 179 10.66       104     71          14         89    81    Medium  25
## 180  7.78       144     25           3         70   116    Medium  77
## 181  4.94       137    112          15        434   149       Bad  66
## 182  7.43       121     83           0         79    91    Medium  68
## 183  4.74       137     60           4        230   140       Bad  25
## 184  5.32       118     74           6        426   102    Medium  80
## 185  9.95       132     33           7         35    97    Medium  60
## 186 10.07       130    100          11        449   107    Medium  64
## 187  8.68       120     51           0         93    86    Medium  46
## 188  6.03       117     32           0        142    96       Bad  62
## 189  8.07       116     37           0        426    90    Medium  76
## 190 12.11       118    117          18        509   104    Medium  26
## 191  8.79       130     37          13        297   101    Medium  37
## 192  6.67       156     42          13        170   173      Good  74
## 193  7.56       108     26           0        408    93    Medium  56
## 194 13.28       139     70           7         71    96      Good  61
## 195  7.23       112     98          18        481   128    Medium  45
## 196  4.19       117     93           4        420   112       Bad  66
## 197  4.10       130     28           6        410   133       Bad  72
## 198  2.52       124     61           0        333   138    Medium  76
## 199  3.62       112     80           5        500   128    Medium  69
## 200  6.42       122     88           5        335   126    Medium  64
## 201  5.56       144     92           0        349   146    Medium  62
## 202  5.94       138     83           0        139   134    Medium  54
## 203  4.10       121     78           4        413   130       Bad  46
## 204  2.05       131     82           0        132   157       Bad  25
## 205  8.74       155     80           0        237   124    Medium  37
## 206  5.68       113     22           1        317   132    Medium  28
## 207  4.97       162     67           0         27   160    Medium  77
## 208  8.19       111    105           0        466    97       Bad  61
## 209  7.78        86     54           0        497    64       Bad  33
## 210  3.02        98     21          11        326    90       Bad  76
## 211  4.36       125     41           2        357   123       Bad  47
## 212  9.39       117    118          14        445   120    Medium  32
## 213 12.04       145     69          19        501   105    Medium  45
## 214  8.23       149     84           5        220   139    Medium  33
## 215  4.83       115    115           3         48   107    Medium  73
## 216  2.34       116     83          15        170   144       Bad  71
## 217  5.73       141     33           0        243   144    Medium  34
## 218  4.34       106     44           0        481   111    Medium  70
## 219  9.70       138     61          12        156   120    Medium  25
## 220 10.62       116     79          19        359   116      Good  58
## 221 10.59       131    120          15        262   124    Medium  30
## 222  6.43       124     44           0        125   107    Medium  80
## 223  7.49       136    119           6        178   145    Medium  35
## 224  3.45       110     45           9        276   125    Medium  62
## 225  4.10       134     82           0        464   141    Medium  48
## 226  6.68       107     25           0        412    82       Bad  36
## 227  7.80       119     33           0        245   122      Good  56
## 228  8.69       113     64          10         68   101    Medium  57
## 229  5.40       149     73          13        381   163       Bad  26
## 230 11.19        98    104           0        404    72    Medium  27
## 231  5.16       115     60           0        119   114       Bad  38
## 232  8.09       132     69           0        123   122    Medium  27
## 233 13.14       137     80          10         24   105      Good  61
## 234  8.65       123     76          18        218   120    Medium  29
## 235  9.43       115     62          11        289   129      Good  56
## 236  5.53       126     32           8         95   132    Medium  50
## 237  9.32       141     34          16        361   108    Medium  69
## 238  9.62       151     28           8        499   135    Medium  48
## 239  7.36       121     24           0        200   133      Good  73
## 240  3.89       123    105           0        149   118       Bad  62
## 241 10.31       159     80           0        362   121    Medium  26
## 242 12.01       136     63           0        160    94    Medium  38
## 243  4.68       124     46           0        199   135    Medium  52
## 244  7.82       124     25          13         87   110    Medium  57
## 245  8.78       130     30           0        391   100    Medium  26
## 246 10.00       114     43           0        199    88      Good  57
## 247  6.90       120     56          20        266    90       Bad  78
## 248  5.04       123    114           0        298   151       Bad  34
## 249  5.36       111     52           0         12   101    Medium  61
## 250  5.05       125     67           0         86   117       Bad  65
## 251  9.16       137    105          10        435   156      Good  72
## 252  3.72       139    111           5        310   132       Bad  62
## 253  8.31       133     97           0         70   117    Medium  32
## 254  5.64       124     24           5        288   122    Medium  57
## 255  9.58       108    104          23        353   129      Good  37
## 256  7.71       123     81           8        198    81       Bad  80
## 257  4.20       147     40           0        277   144    Medium  73
## 258  8.67       125     62          14        477   112    Medium  80
## 259  3.47       108     38           0        251    81       Bad  72
## 260  5.12       123     36          10        467   100       Bad  74
## 261  7.67       129    117           8        400   101       Bad  36
## 262  5.71       121     42           4        188   118    Medium  54
## 263  6.37       120     77          15         86   132    Medium  48
## 264  7.77       116     26           6        434   115    Medium  25
## 265  6.95       128     29           5        324   159      Good  31
## 266  5.31       130     35          10        402   129       Bad  39
## 267  9.10       128     93          12        343   112      Good  73
## 268  5.83       134     82           7        473   112       Bad  51
## 269  6.53       123     57           0         66   105    Medium  39
## 270  5.01       159     69           0        438   166    Medium  46
## 271 11.99       119     26           0        284    89      Good  26
## 272  4.55       111     56           0        504   110    Medium  62
## 273 12.98       113     33           0         14    63      Good  38
## 274 10.04       116    106           8        244    86    Medium  58
## 275  7.22       135     93           2         67   119    Medium  34
## 276  6.67       107    119          11        210   132    Medium  53
## 277  6.93       135     69          14        296   130    Medium  73
## 278  7.80       136     48          12        326   125    Medium  36
## 279  7.22       114    113           2        129   151      Good  40
## 280  3.42       141     57          13        376   158    Medium  64
## 281  2.86       121     86          10        496   145       Bad  51
## 282 11.19       122     69           7        303   105      Good  45
## 283  7.74       150     96           0         80   154      Good  61
## 284  5.36       135    110           0        112   117    Medium  80
## 285  6.97       106     46          11        414    96       Bad  79
## 286  7.60       146     26          11        261   131    Medium  39
## 287  7.53       117    118          11        429   113    Medium  67
## 288  6.88        95     44           4        208    72       Bad  44
## 289  6.98       116     40           0         74    97    Medium  76
## 290  8.75       143     77          25        448   156    Medium  43
## 291  9.49       107    111          14        400   103    Medium  41
## 292  6.64       118     70           0        106    89       Bad  39
## 293 11.82       113     66          16        322    74      Good  76
## 294 11.28       123     84           0         74    89      Good  59
## 295 12.66       148     76           3        126    99      Good  60
## 296  4.21       118     35          14        502   137    Medium  79
## 297  8.21       127     44          13        160   123      Good  63
## 298  3.07       118     83          13        276   104       Bad  75
## 299 10.98       148     63           0        312   130      Good  63
## 300  9.40       135     40          17        497    96    Medium  54
## 301  8.57       116     78           1        158    99    Medium  45
## 302  7.41        99     93           0        198    87    Medium  57
## 303  5.28       108     77          13        388   110       Bad  74
## 304 10.01       133     52          16        290    99    Medium  43
## 305 11.93       123     98          12        408   134      Good  29
## 306  8.03       115     29          26        394   132    Medium  33
## 307  4.78       131     32           1         85   133    Medium  48
## 308  5.90       138     92           0         13   120       Bad  61
## 309  9.24       126     80          19        436   126    Medium  52
## 310 11.18       131    111          13         33    80       Bad  68
## 311  9.53       175     65          29        419   166    Medium  53
## 312  6.15       146     68          12        328   132       Bad  51
## 313  6.80       137    117           5        337   135       Bad  38
## 314  9.33       103     81           3        491    54    Medium  66
## 315  7.72       133     33          10        333   129      Good  71
## 316  6.39       131     21           8        220   171      Good  29
## 317 15.63       122     36           5        369    72      Good  35
## 318  6.41       142     30           0        472   136      Good  80
## 319 10.08       116     72          10        456   130      Good  41
## 320  6.97       127     45          19        459   129    Medium  57
## 321  5.86       136     70          12        171   152    Medium  44
## 322  7.52       123     39           5        499    98    Medium  34
## 323  9.16       140     50          10        300   139      Good  60
## 324 10.36       107    105          18        428   103    Medium  34
## 325  2.66       136     65           4        133   150       Bad  53
## 326 11.70       144     69          11        131   104    Medium  47
## 327  4.69       133     30           0        152   122    Medium  53
## 328  6.23       112     38          17        316   104    Medium  80
## 329  3.15       117     66           1         65   111       Bad  55
## 330 11.27       100     54           9        433    89      Good  45
## 331  4.99       122     59           0        501   112       Bad  32
## 332 10.10       135     63          15        213   134    Medium  32
## 333  5.74       106     33          20        354   104    Medium  61
## 334  5.87       136     60           7        303   147    Medium  41
## 335  7.63        93    117           9        489    83       Bad  42
## 336  6.18       120     70          15        464   110    Medium  72
## 337  5.17       138     35           6         60   143       Bad  28
## 338  8.61       130     38           0        283   102    Medium  80
## 339  5.97       112     24           0        164   101    Medium  45
## 340 11.54       134     44           4        219   126      Good  44
## 341  7.50       140     29           0        105    91       Bad  43
## 342  7.38        98    120           0        268    93    Medium  72
## 343  7.81       137    102          13        422   118    Medium  71
## 344  5.99       117     42          10        371   121       Bad  26
## 345  8.43       138     80           0        108   126      Good  70
## 346  4.81       121     68           0        279   149      Good  79
## 347  8.97       132    107           0        144   125    Medium  33
## 348  6.88        96     39           0        161   112      Good  27
## 349 12.57       132    102          20        459   107      Good  49
## 350  9.32       134     27          18        467    96    Medium  49
## 351  8.64       111    101          17        266    91    Medium  63
## 352 10.44       124    115          16        458   105    Medium  62
## 353 13.44       133    103          14        288   122      Good  61
## 354  9.45       107     67          12        430    92    Medium  35
## 355  5.30       133     31           1         80   145    Medium  42
## 356  7.02       130    100           0        306   146      Good  42
## 357  3.58       142    109           0        111   164      Good  72
## 358 13.36       103     73           3        276    72    Medium  34
## 359  4.17       123     96          10         71   118       Bad  69
## 360  3.13       130     62          11        396   130       Bad  66
## 361  8.77       118     86           7        265   114      Good  52
## 362  8.68       131     25          10        183   104    Medium  56
## 363  5.25       131     55           0         26   110       Bad  79
## 364 10.26       111     75           1        377   108      Good  25
## 365 10.50       122     21          16        488   131      Good  30
## 366  6.53       154     30           0        122   162    Medium  57
## 367  5.98       124     56          11        447   134    Medium  53
## 368 14.37        95    106           0        256    53      Good  52
## 369 10.71       109     22          10        348    79      Good  74
## 370 10.26       135    100          22        463   122    Medium  36
## 371  7.68       126     41          22        403   119       Bad  42
## 372  9.08       152     81           0        191   126    Medium  54
## 373  7.80       121     50           0        508    98    Medium  65
## 374  5.58       137     71           0        402   116    Medium  78
## 375  9.44       131     47           7         90   118    Medium  47
## 376  7.90       132     46           4        206   124    Medium  73
## 377 16.27       141     60          19        319    92      Good  44
## 378  6.81       132     61           0        263   125    Medium  41
## 379  6.11       133     88           3        105   119    Medium  79
## 380  5.81       125    111           0        404   107       Bad  54
## 381  9.64       106     64          10         17    89    Medium  68
## 382  3.90       124     65          21        496   151       Bad  77
## 383  4.95       121     28          19        315   121    Medium  66
## 384  9.35        98    117           0         76    68    Medium  63
## 385 12.85       123     37          15        348   112      Good  28
## 386  5.87       131     73          13        455   132    Medium  62
## 387  5.32       152    116           0        170   160    Medium  39
## 388  8.67       142     73          14        238   115    Medium  73
## 389  8.14       135     89          11        245    78       Bad  79
## 390  8.44       128     42           8        328   107    Medium  35
## 391  5.47       108     75           9         61   111    Medium  67
## 392  6.10       153     63           0         49   124       Bad  56
## 393  4.53       129     42          13        315   130       Bad  34
## 394  5.57       109     51          10         26   120    Medium  30
## 395  5.35       130     58          19        366   139       Bad  33
## 396 12.57       138    108          17        203   128      Good  33
## 397  6.14       139     23           3         37   120    Medium  55
## 398  7.41       162     26          12        368   159    Medium  40
## 399  5.94       100     79           7        284    95       Bad  50
## 400  9.71       134     37           0         27   120      Good  49
##     Education Urban  US
## 1          17   Yes Yes
## 2          10   Yes Yes
## 3          12   Yes Yes
## 4          14   Yes Yes
## 5          13   Yes  No
## 6          16    No Yes
## 7          15   Yes  No
## 8          10   Yes Yes
## 9          10    No  No
## 10         17    No Yes
## 11         10    No Yes
## 12         13   Yes Yes
## 13         18   Yes  No
## 14         18   Yes Yes
## 15         18   Yes Yes
## 16         18    No  No
## 17         13   Yes  No
## 18         10   Yes Yes
## 19         17    No Yes
## 20         12   Yes Yes
## 21         18   Yes Yes
## 22         18    No Yes
## 23         13   Yes  No
## 24         10   Yes  No
## 25         12   Yes Yes
## 26         11    No  No
## 27         11    No Yes
## 28         17   Yes  No
## 29         11   Yes Yes
## 30         17   Yes Yes
## 31         12   Yes  No
## 32         18   Yes Yes
## 33         10    No Yes
## 34         16   Yes Yes
## 35         17   Yes Yes
## 36         17    No Yes
## 37         18    No  No
## 38         10   Yes Yes
## 39         15   Yes  No
## 40         10    No  No
## 41         17    No  No
## 42         16   Yes  No
## 43         18   Yes  No
## 44         13   Yes Yes
## 45         13   Yes Yes
## 46         12   Yes Yes
## 47         15    No Yes
## 48         16   Yes  No
## 49         18   Yes  No
## 50         17   Yes  No
## 51         16   Yes Yes
## 52         16   Yes  No
## 53         18   Yes Yes
## 54         17   Yes Yes
## 55         17    No Yes
## 56         18   Yes Yes
## 57         17   Yes  No
## 58         11   Yes  No
## 59         16   Yes Yes
## 60         13   Yes  No
## 61         13   Yes Yes
## 62         13    No  No
## 63         17   Yes Yes
## 64         13   Yes Yes
## 65         16    No Yes
## 66         13    No  No
## 67         18   Yes  No
## 68         16   Yes Yes
## 69         13   Yes Yes
## 70         12   Yes  No
## 71         12   Yes Yes
## 72         17    No Yes
## 73         15   Yes  No
## 74         11    No Yes
## 75         13    No Yes
## 76         16    No Yes
## 77         15   Yes Yes
## 78         18    No Yes
## 79         12   Yes Yes
## 80         13   Yes  No
## 81         11   Yes Yes
## 82         13   Yes  No
## 83         17   Yes Yes
## 84         11   Yes Yes
## 85         18    No  No
## 86         13    No  No
## 87         15   Yes  No
## 88         16    No Yes
## 89         10   Yes Yes
## 90         16    No  No
## 91         11    No  No
## 92         15   Yes Yes
## 93         12   Yes  No
## 94         17   Yes  No
## 95         11   Yes Yes
## 96         13   Yes Yes
## 97         16    No Yes
## 98         16   Yes Yes
## 99         16    No Yes
## 100        16    No Yes
## 101        12    No Yes
## 102        18   Yes  No
## 103        16    No  No
## 104        17   Yes Yes
## 105        12   Yes  No
## 106        11   Yes Yes
## 107        18    No  No
## 108        12   Yes  No
## 109        16   Yes  No
## 110        17    No  No
## 111        14   Yes Yes
## 112        14   Yes Yes
## 113        12   Yes Yes
## 114        12   Yes Yes
## 115        13   Yes Yes
## 116        13   Yes  No
## 117        10    No  No
## 118        12   Yes  No
## 119        11   Yes Yes
## 120        12   Yes Yes
## 121        13   Yes Yes
## 122        10   Yes Yes
## 123        10   Yes Yes
## 124        15    No Yes
## 125        14   Yes  No
## 126        15    No  No
## 127        16   Yes Yes
## 128        14   Yes Yes
## 129        13   Yes Yes
## 130        10    No Yes
## 131        12   Yes Yes
## 132        16   Yes  No
## 133        10   Yes Yes
## 134        12   Yes Yes
## 135        16   Yes  No
## 136        18    No Yes
## 137        18    No  No
## 138        11   Yes  No
## 139        10   Yes Yes
## 140        13    No Yes
## 141        18   Yes Yes
## 142        15   Yes  No
## 143        15   Yes  No
## 144        17   Yes Yes
## 145        11    No  No
## 146        17   Yes Yes
## 147        14   Yes  No
## 148        16    No Yes
## 149        14    No Yes
## 150        11   Yes Yes
## 151        10    No Yes
## 152        17    No Yes
## 153        13    No  No
## 154        17    No Yes
## 155        16    No Yes
## 156        16   Yes  No
## 157        16   Yes  No
## 158        13    No Yes
## 159        10    No Yes
## 160        18    No  No
## 161        12    No  No
## 162        12    No Yes
## 163        13   Yes  No
## 164        17    No  No
## 165        13    No Yes
## 166        15   Yes Yes
## 167        11   Yes Yes
## 168        13   Yes  No
## 169        10   Yes  No
## 170        18   Yes Yes
## 171        10   Yes Yes
## 172        15   Yes Yes
## 173        16   Yes Yes
## 174        18   Yes Yes
## 175        15    No  No
## 176        12   Yes  No
## 177        11    No Yes
## 178        17   Yes Yes
## 179        14    No Yes
## 180        18   Yes Yes
## 181        13   Yes Yes
## 182        11   Yes  No
## 183        13   Yes  No
## 184        18   Yes Yes
## 185        11    No Yes
## 186        10   Yes Yes
## 187        17    No  No
## 188        17   Yes  No
## 189        15   Yes  No
## 190        15    No Yes
## 191        13    No Yes
## 192        14   Yes Yes
## 193        14    No  No
## 194        10   Yes Yes
## 195        11   Yes Yes
## 196        11   Yes Yes
## 197        16   Yes Yes
## 198        16   Yes  No
## 199        10   Yes Yes
## 200        14   Yes Yes
## 201        12    No  No
## 202        18   Yes  No
## 203        10    No Yes
## 204        14   Yes  No
## 205        14   Yes  No
## 206        12   Yes  No
## 207        17   Yes Yes
## 208        10    No  No
## 209        12   Yes  No
## 210        11    No Yes
## 211        14    No Yes
## 212        15   Yes Yes
## 213        11   Yes Yes
## 214        10   Yes Yes
## 215        18   Yes Yes
## 216        11   Yes Yes
## 217        17   Yes  No
## 218        14    No  No
## 219        14   Yes Yes
## 220        17   Yes Yes
## 221        10   Yes Yes
## 222        11   Yes  No
## 223        13   Yes Yes
## 224        14   Yes Yes
## 225        13    No  No
## 226        14   Yes  No
## 227        14   Yes  No
## 228        16   Yes Yes
## 229        11    No Yes
## 230        18    No  No
## 231        14    No  No
## 232        11    No  No
## 233        15   Yes Yes
## 234        14    No Yes
## 235        16    No Yes
## 236        17   Yes Yes
## 237        10   Yes Yes
## 238        10   Yes Yes
## 239        13   Yes  No
## 240        16   Yes Yes
## 241        18   Yes  No
## 242        12   Yes  No
## 243        14    No  No
## 244        10   Yes Yes
## 245        18   Yes  No
## 246        10    No Yes
## 247        18   Yes Yes
## 248        16   Yes  No
## 249        11   Yes Yes
## 250        11   Yes  No
## 251        14   Yes Yes
## 252        13   Yes Yes
## 253        16   Yes  No
## 254        12    No Yes
## 255        17   Yes Yes
## 256        15   Yes Yes
## 257        10   Yes  No
## 258        13   Yes Yes
## 259        14    No  No
## 260        11    No Yes
## 261        10   Yes Yes
## 262        15   Yes Yes
## 263        18   Yes Yes
## 264        17   Yes Yes
## 265        15   Yes Yes
## 266        17   Yes Yes
## 267        17    No Yes
## 268        12    No Yes
## 269        11   Yes  No
## 270        17   Yes  No
## 271        10   Yes  No
## 272        16   Yes  No
## 273        12   Yes  No
## 274        12   Yes Yes
## 275        11   Yes Yes
## 276        11   Yes Yes
## 277        15   Yes Yes
## 278        16   Yes Yes
## 279        15    No Yes
## 280        18   Yes Yes
## 281        10   Yes Yes
## 282        16    No Yes
## 283        11   Yes  No
## 284        16    No  No
## 285        17    No  No
## 286        10   Yes Yes
## 287        18    No Yes
## 288        17   Yes Yes
## 289        15    No  No
## 290        17   Yes Yes
## 291        11    No Yes
## 292        17   Yes  No
## 293        15   Yes Yes
## 294        10   Yes  No
## 295        11   Yes Yes
## 296        10    No Yes
## 297        18   Yes Yes
## 298        10   Yes Yes
## 299        15   Yes  No
## 300        17    No Yes
## 301        11   Yes Yes
## 302        16   Yes Yes
## 303        14   Yes Yes
## 304        11   Yes Yes
## 305        10   Yes Yes
## 306        13   Yes Yes
## 307        12   Yes Yes
## 308        12   Yes  No
## 309        10   Yes Yes
## 310        18   Yes Yes
## 311        12   Yes Yes
## 312        14   Yes Yes
## 313        10   Yes Yes
## 314        13   Yes  No
## 315        14   Yes Yes
## 316        14   Yes Yes
## 317        10   Yes Yes
## 318        15    No  No
## 319        14    No Yes
## 320        11    No Yes
## 321        18   Yes Yes
## 322        15   Yes  No
## 323        15   Yes Yes
## 324        12   Yes Yes
## 325        13   Yes Yes
## 326        11   Yes Yes
## 327        17   Yes  No
## 328        16   Yes Yes
## 329        11   Yes Yes
## 330        12   Yes Yes
## 331        14    No  No
## 332        10   Yes Yes
## 333        12   Yes Yes
## 334        10   Yes Yes
## 335        13   Yes Yes
## 336        15   Yes Yes
## 337        18   Yes  No
## 338        15   Yes  No
## 339        11   Yes  No
## 340        15   Yes Yes
## 341        16   Yes  No
## 342        10    No  No
## 343        10    No Yes
## 344        14   Yes Yes
## 345        13    No Yes
## 346        12   Yes  No
## 347        13    No  No
## 348        14    No  No
## 349        11   Yes Yes
## 350        14    No Yes
## 351        17    No Yes
## 352        16    No Yes
## 353        17   Yes Yes
## 354        12    No Yes
## 355        18   Yes Yes
## 356        11   Yes  No
## 357        12   Yes  No
## 358        15   Yes Yes
## 359        11   Yes Yes
## 360        14   Yes Yes
## 361        15    No Yes
## 362        15    No Yes
## 363        12   Yes Yes
## 364        12   Yes  No
## 365        14   Yes Yes
## 366        17    No  No
## 367        12    No Yes
## 368        17   Yes  No
## 369        14    No Yes
## 370        14   Yes Yes
## 371        12   Yes Yes
## 372        16   Yes  No
## 373        11    No  No
## 374        17   Yes  No
## 375        12   Yes Yes
## 376        11   Yes  No
## 377        11   Yes Yes
## 378        12    No  No
## 379        12   Yes Yes
## 380        15   Yes  No
## 381        17   Yes Yes
## 382        13   Yes Yes
## 383        14   Yes Yes
## 384        10   Yes  No
## 385        12   Yes Yes
## 386        17   Yes Yes
## 387        16   Yes  No
## 388        14    No Yes
## 389        16   Yes Yes
## 390        12   Yes Yes
## 391        12   Yes Yes
## 392        16   Yes  No
## 393        13   Yes Yes
## 394        17    No Yes
## 395        16   Yes Yes
## 396        14   Yes Yes
## 397        11    No Yes
## 398        18   Yes Yes
## 399        12   Yes Yes
## 400        16   Yes Yes
attach(Carseats)

Multiple regression model with interaction terms for Carseats dataset:

lm.fit.qual = lm(Sales ~ . + Income:Advertising + Price:Age, data = Carseats)
summary(lm.fit.qual)
## 
## Call:
## lm(formula = Sales ~ . + Income:Advertising + Price:Age, data = Carseats)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9208 -0.7503  0.0177  0.6754  3.3413 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         6.5755654  1.0087470   6.519 2.22e-10 ***
## CompPrice           0.0929371  0.0041183  22.567  < 2e-16 ***
## Income              0.0108940  0.0026044   4.183 3.57e-05 ***
## Advertising         0.0702462  0.0226091   3.107 0.002030 ** 
## Population          0.0001592  0.0003679   0.433 0.665330    
## Price              -0.1008064  0.0074399 -13.549  < 2e-16 ***
## ShelveLocGood       4.8486762  0.1528378  31.724  < 2e-16 ***
## ShelveLocMedium     1.9532620  0.1257682  15.531  < 2e-16 ***
## Age                -0.0579466  0.0159506  -3.633 0.000318 ***
## Education          -0.0208525  0.0196131  -1.063 0.288361    
## UrbanYes            0.1401597  0.1124019   1.247 0.213171    
## USYes              -0.1575571  0.1489234  -1.058 0.290729    
## Income:Advertising  0.0007510  0.0002784   2.698 0.007290 ** 
## Price:Age           0.0001068  0.0001333   0.801 0.423812    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.011 on 386 degrees of freedom
## Multiple R-squared:  0.8761, Adjusted R-squared:  0.8719 
## F-statistic:   210 on 13 and 386 DF,  p-value: < 2.2e-16
contrasts(ShelveLoc)
##        Good Medium
## Bad       0      0
## Good      1      0
## Medium    0      1

========================EXERCISE========================

names(Auto)
## [1] "mpg"          "cylinders"    "displacement" "horsepower"  
## [5] "weight"       "acceleration" "year"         "origin"      
## [9] "name"
summary(Auto)
##       mpg          cylinders      displacement     horsepower   
##  Min.   : 9.00   Min.   :3.000   Min.   : 68.0   Min.   : 46.0  
##  1st Qu.:17.00   1st Qu.:4.000   1st Qu.:105.0   1st Qu.: 75.0  
##  Median :22.75   Median :4.000   Median :151.0   Median : 93.5  
##  Mean   :23.45   Mean   :5.472   Mean   :194.4   Mean   :104.5  
##  3rd Qu.:29.00   3rd Qu.:8.000   3rd Qu.:275.8   3rd Qu.:126.0  
##  Max.   :46.60   Max.   :8.000   Max.   :455.0   Max.   :230.0  
##                                                                 
##      weight      acceleration        year           origin     
##  Min.   :1613   Min.   : 8.00   Min.   :70.00   Min.   :1.000  
##  1st Qu.:2225   1st Qu.:13.78   1st Qu.:73.00   1st Qu.:1.000  
##  Median :2804   Median :15.50   Median :76.00   Median :1.000  
##  Mean   :2978   Mean   :15.54   Mean   :75.98   Mean   :1.577  
##  3rd Qu.:3615   3rd Qu.:17.02   3rd Qu.:79.00   3rd Qu.:2.000  
##  Max.   :5140   Max.   :24.80   Max.   :82.00   Max.   :3.000  
##                                                                
##                  name    
##  amc matador       :  5  
##  ford pinto        :  5  
##  toyota corolla    :  5  
##  amc gremlin       :  4  
##  amc hornet        :  4  
##  chevrolet chevette:  4  
##  (Other)           :365
head(Auto, n=10)
##    mpg cylinders displacement horsepower weight acceleration year origin
## 1   18         8          307        130   3504         12.0   70      1
## 2   15         8          350        165   3693         11.5   70      1
## 3   18         8          318        150   3436         11.0   70      1
## 4   16         8          304        150   3433         12.0   70      1
## 5   17         8          302        140   3449         10.5   70      1
## 6   15         8          429        198   4341         10.0   70      1
## 7   14         8          454        220   4354          9.0   70      1
## 8   14         8          440        215   4312          8.5   70      1
## 9   14         8          455        225   4425         10.0   70      1
## 10  15         8          390        190   3850          8.5   70      1
##                         name
## 1  chevrolet chevelle malibu
## 2          buick skylark 320
## 3         plymouth satellite
## 4              amc rebel sst
## 5                ford torino
## 6           ford galaxie 500
## 7           chevrolet impala
## 8          plymouth fury iii
## 9           pontiac catalina
## 10        amc ambassador dpl
attach(Auto)
lm.fit.auto = lm(mpg ~ horsepower, data = Auto)
summary(lm.fit.auto)
## 
## Call:
## lm(formula = mpg ~ horsepower, data = Auto)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.5710  -3.2592  -0.3435   2.7630  16.9240 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39.935861   0.717499   55.66   <2e-16 ***
## horsepower  -0.157845   0.006446  -24.49   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.906 on 390 degrees of freedom
## Multiple R-squared:  0.6059, Adjusted R-squared:  0.6049 
## F-statistic: 599.7 on 1 and 390 DF,  p-value: < 2.2e-16
mean(mpg)
## [1] 23.44592
plot(horsepower, mpg)
abline(h=mean(mpg))
abline(lm.fit.auto, col = "blue")

plot(lm.fit.auto)

# prediction
predict(lm.fit.auto ,data.frame(horsepower=c(98)),interval ="confidence")
##        fit      lwr      upr
## 1 24.46708 23.97308 24.96108
predict(lm.fit.auto ,data.frame(horsepower=c(98)),interval ="prediction")
##        fit     lwr      upr
## 1 24.46708 14.8094 34.12476

ISLR: 3.9.

auto.without.name = Auto[1:8]
auto.without.name
##      mpg cylinders displacement horsepower weight acceleration year origin
## 1   18.0         8        307.0        130   3504         12.0   70      1
## 2   15.0         8        350.0        165   3693         11.5   70      1
## 3   18.0         8        318.0        150   3436         11.0   70      1
## 4   16.0         8        304.0        150   3433         12.0   70      1
## 5   17.0         8        302.0        140   3449         10.5   70      1
## 6   15.0         8        429.0        198   4341         10.0   70      1
## 7   14.0         8        454.0        220   4354          9.0   70      1
## 8   14.0         8        440.0        215   4312          8.5   70      1
## 9   14.0         8        455.0        225   4425         10.0   70      1
## 10  15.0         8        390.0        190   3850          8.5   70      1
## 11  15.0         8        383.0        170   3563         10.0   70      1
## 12  14.0         8        340.0        160   3609          8.0   70      1
## 13  15.0         8        400.0        150   3761          9.5   70      1
## 14  14.0         8        455.0        225   3086         10.0   70      1
## 15  24.0         4        113.0         95   2372         15.0   70      3
## 16  22.0         6        198.0         95   2833         15.5   70      1
## 17  18.0         6        199.0         97   2774         15.5   70      1
## 18  21.0         6        200.0         85   2587         16.0   70      1
## 19  27.0         4         97.0         88   2130         14.5   70      3
## 20  26.0         4         97.0         46   1835         20.5   70      2
## 21  25.0         4        110.0         87   2672         17.5   70      2
## 22  24.0         4        107.0         90   2430         14.5   70      2
## 23  25.0         4        104.0         95   2375         17.5   70      2
## 24  26.0         4        121.0        113   2234         12.5   70      2
## 25  21.0         6        199.0         90   2648         15.0   70      1
## 26  10.0         8        360.0        215   4615         14.0   70      1
## 27  10.0         8        307.0        200   4376         15.0   70      1
## 28  11.0         8        318.0        210   4382         13.5   70      1
## 29   9.0         8        304.0        193   4732         18.5   70      1
## 30  27.0         4         97.0         88   2130         14.5   71      3
## 31  28.0         4        140.0         90   2264         15.5   71      1
## 32  25.0         4        113.0         95   2228         14.0   71      3
## 34  19.0         6        232.0        100   2634         13.0   71      1
## 35  16.0         6        225.0        105   3439         15.5   71      1
## 36  17.0         6        250.0        100   3329         15.5   71      1
## 37  19.0         6        250.0         88   3302         15.5   71      1
## 38  18.0         6        232.0        100   3288         15.5   71      1
## 39  14.0         8        350.0        165   4209         12.0   71      1
## 40  14.0         8        400.0        175   4464         11.5   71      1
## 41  14.0         8        351.0        153   4154         13.5   71      1
## 42  14.0         8        318.0        150   4096         13.0   71      1
## 43  12.0         8        383.0        180   4955         11.5   71      1
## 44  13.0         8        400.0        170   4746         12.0   71      1
## 45  13.0         8        400.0        175   5140         12.0   71      1
## 46  18.0         6        258.0        110   2962         13.5   71      1
## 47  22.0         4        140.0         72   2408         19.0   71      1
## 48  19.0         6        250.0        100   3282         15.0   71      1
## 49  18.0         6        250.0         88   3139         14.5   71      1
## 50  23.0         4        122.0         86   2220         14.0   71      1
## 51  28.0         4        116.0         90   2123         14.0   71      2
## 52  30.0         4         79.0         70   2074         19.5   71      2
## 53  30.0         4         88.0         76   2065         14.5   71      2
## 54  31.0         4         71.0         65   1773         19.0   71      3
## 55  35.0         4         72.0         69   1613         18.0   71      3
## 56  27.0         4         97.0         60   1834         19.0   71      2
## 57  26.0         4         91.0         70   1955         20.5   71      1
## 58  24.0         4        113.0         95   2278         15.5   72      3
## 59  25.0         4         97.5         80   2126         17.0   72      1
## 60  23.0         4         97.0         54   2254         23.5   72      2
## 61  20.0         4        140.0         90   2408         19.5   72      1
## 62  21.0         4        122.0         86   2226         16.5   72      1
## 63  13.0         8        350.0        165   4274         12.0   72      1
## 64  14.0         8        400.0        175   4385         12.0   72      1
## 65  15.0         8        318.0        150   4135         13.5   72      1
## 66  14.0         8        351.0        153   4129         13.0   72      1
## 67  17.0         8        304.0        150   3672         11.5   72      1
## 68  11.0         8        429.0        208   4633         11.0   72      1
## 69  13.0         8        350.0        155   4502         13.5   72      1
## 70  12.0         8        350.0        160   4456         13.5   72      1
## 71  13.0         8        400.0        190   4422         12.5   72      1
## 72  19.0         3         70.0         97   2330         13.5   72      3
## 73  15.0         8        304.0        150   3892         12.5   72      1
## 74  13.0         8        307.0        130   4098         14.0   72      1
## 75  13.0         8        302.0        140   4294         16.0   72      1
## 76  14.0         8        318.0        150   4077         14.0   72      1
## 77  18.0         4        121.0        112   2933         14.5   72      2
## 78  22.0         4        121.0         76   2511         18.0   72      2
## 79  21.0         4        120.0         87   2979         19.5   72      2
## 80  26.0         4         96.0         69   2189         18.0   72      2
## 81  22.0         4        122.0         86   2395         16.0   72      1
## 82  28.0         4         97.0         92   2288         17.0   72      3
## 83  23.0         4        120.0         97   2506         14.5   72      3
## 84  28.0         4         98.0         80   2164         15.0   72      1
## 85  27.0         4         97.0         88   2100         16.5   72      3
## 86  13.0         8        350.0        175   4100         13.0   73      1
## 87  14.0         8        304.0        150   3672         11.5   73      1
## 88  13.0         8        350.0        145   3988         13.0   73      1
## 89  14.0         8        302.0        137   4042         14.5   73      1
## 90  15.0         8        318.0        150   3777         12.5   73      1
## 91  12.0         8        429.0        198   4952         11.5   73      1
## 92  13.0         8        400.0        150   4464         12.0   73      1
## 93  13.0         8        351.0        158   4363         13.0   73      1
## 94  14.0         8        318.0        150   4237         14.5   73      1
## 95  13.0         8        440.0        215   4735         11.0   73      1
## 96  12.0         8        455.0        225   4951         11.0   73      1
## 97  13.0         8        360.0        175   3821         11.0   73      1
## 98  18.0         6        225.0        105   3121         16.5   73      1
## 99  16.0         6        250.0        100   3278         18.0   73      1
## 100 18.0         6        232.0        100   2945         16.0   73      1
## 101 18.0         6        250.0         88   3021         16.5   73      1
## 102 23.0         6        198.0         95   2904         16.0   73      1
## 103 26.0         4         97.0         46   1950         21.0   73      2
## 104 11.0         8        400.0        150   4997         14.0   73      1
## 105 12.0         8        400.0        167   4906         12.5   73      1
## 106 13.0         8        360.0        170   4654         13.0   73      1
## 107 12.0         8        350.0        180   4499         12.5   73      1
## 108 18.0         6        232.0        100   2789         15.0   73      1
## 109 20.0         4         97.0         88   2279         19.0   73      3
## 110 21.0         4        140.0         72   2401         19.5   73      1
## 111 22.0         4        108.0         94   2379         16.5   73      3
## 112 18.0         3         70.0         90   2124         13.5   73      3
## 113 19.0         4        122.0         85   2310         18.5   73      1
## 114 21.0         6        155.0        107   2472         14.0   73      1
## 115 26.0         4         98.0         90   2265         15.5   73      2
## 116 15.0         8        350.0        145   4082         13.0   73      1
## 117 16.0         8        400.0        230   4278          9.5   73      1
## 118 29.0         4         68.0         49   1867         19.5   73      2
## 119 24.0         4        116.0         75   2158         15.5   73      2
## 120 20.0         4        114.0         91   2582         14.0   73      2
## 121 19.0         4        121.0        112   2868         15.5   73      2
## 122 15.0         8        318.0        150   3399         11.0   73      1
## 123 24.0         4        121.0        110   2660         14.0   73      2
## 124 20.0         6        156.0        122   2807         13.5   73      3
## 125 11.0         8        350.0        180   3664         11.0   73      1
## 126 20.0         6        198.0         95   3102         16.5   74      1
## 128 19.0         6        232.0        100   2901         16.0   74      1
## 129 15.0         6        250.0        100   3336         17.0   74      1
## 130 31.0         4         79.0         67   1950         19.0   74      3
## 131 26.0         4        122.0         80   2451         16.5   74      1
## 132 32.0         4         71.0         65   1836         21.0   74      3
## 133 25.0         4        140.0         75   2542         17.0   74      1
## 134 16.0         6        250.0        100   3781         17.0   74      1
## 135 16.0         6        258.0        110   3632         18.0   74      1
## 136 18.0         6        225.0        105   3613         16.5   74      1
## 137 16.0         8        302.0        140   4141         14.0   74      1
## 138 13.0         8        350.0        150   4699         14.5   74      1
## 139 14.0         8        318.0        150   4457         13.5   74      1
## 140 14.0         8        302.0        140   4638         16.0   74      1
## 141 14.0         8        304.0        150   4257         15.5   74      1
## 142 29.0         4         98.0         83   2219         16.5   74      2
## 143 26.0         4         79.0         67   1963         15.5   74      2
## 144 26.0         4         97.0         78   2300         14.5   74      2
## 145 31.0         4         76.0         52   1649         16.5   74      3
## 146 32.0         4         83.0         61   2003         19.0   74      3
## 147 28.0         4         90.0         75   2125         14.5   74      1
## 148 24.0         4         90.0         75   2108         15.5   74      2
## 149 26.0         4        116.0         75   2246         14.0   74      2
## 150 24.0         4        120.0         97   2489         15.0   74      3
## 151 26.0         4        108.0         93   2391         15.5   74      3
## 152 31.0         4         79.0         67   2000         16.0   74      2
## 153 19.0         6        225.0         95   3264         16.0   75      1
## 154 18.0         6        250.0        105   3459         16.0   75      1
## 155 15.0         6        250.0         72   3432         21.0   75      1
## 156 15.0         6        250.0         72   3158         19.5   75      1
## 157 16.0         8        400.0        170   4668         11.5   75      1
## 158 15.0         8        350.0        145   4440         14.0   75      1
## 159 16.0         8        318.0        150   4498         14.5   75      1
## 160 14.0         8        351.0        148   4657         13.5   75      1
## 161 17.0         6        231.0        110   3907         21.0   75      1
## 162 16.0         6        250.0        105   3897         18.5   75      1
## 163 15.0         6        258.0        110   3730         19.0   75      1
## 164 18.0         6        225.0         95   3785         19.0   75      1
## 165 21.0         6        231.0        110   3039         15.0   75      1
## 166 20.0         8        262.0        110   3221         13.5   75      1
## 167 13.0         8        302.0        129   3169         12.0   75      1
## 168 29.0         4         97.0         75   2171         16.0   75      3
## 169 23.0         4        140.0         83   2639         17.0   75      1
## 170 20.0         6        232.0        100   2914         16.0   75      1
## 171 23.0         4        140.0         78   2592         18.5   75      1
## 172 24.0         4        134.0         96   2702         13.5   75      3
## 173 25.0         4         90.0         71   2223         16.5   75      2
## 174 24.0         4        119.0         97   2545         17.0   75      3
## 175 18.0         6        171.0         97   2984         14.5   75      1
## 176 29.0         4         90.0         70   1937         14.0   75      2
## 177 19.0         6        232.0         90   3211         17.0   75      1
## 178 23.0         4        115.0         95   2694         15.0   75      2
## 179 23.0         4        120.0         88   2957         17.0   75      2
## 180 22.0         4        121.0         98   2945         14.5   75      2
## 181 25.0         4        121.0        115   2671         13.5   75      2
## 182 33.0         4         91.0         53   1795         17.5   75      3
## 183 28.0         4        107.0         86   2464         15.5   76      2
## 184 25.0         4        116.0         81   2220         16.9   76      2
## 185 25.0         4        140.0         92   2572         14.9   76      1
## 186 26.0         4         98.0         79   2255         17.7   76      1
## 187 27.0         4        101.0         83   2202         15.3   76      2
## 188 17.5         8        305.0        140   4215         13.0   76      1
## 189 16.0         8        318.0        150   4190         13.0   76      1
## 190 15.5         8        304.0        120   3962         13.9   76      1
## 191 14.5         8        351.0        152   4215         12.8   76      1
## 192 22.0         6        225.0        100   3233         15.4   76      1
## 193 22.0         6        250.0        105   3353         14.5   76      1
## 194 24.0         6        200.0         81   3012         17.6   76      1
## 195 22.5         6        232.0         90   3085         17.6   76      1
## 196 29.0         4         85.0         52   2035         22.2   76      1
## 197 24.5         4         98.0         60   2164         22.1   76      1
## 198 29.0         4         90.0         70   1937         14.2   76      2
## 199 33.0         4         91.0         53   1795         17.4   76      3
## 200 20.0         6        225.0        100   3651         17.7   76      1
## 201 18.0         6        250.0         78   3574         21.0   76      1
## 202 18.5         6        250.0        110   3645         16.2   76      1
## 203 17.5         6        258.0         95   3193         17.8   76      1
## 204 29.5         4         97.0         71   1825         12.2   76      2
## 205 32.0         4         85.0         70   1990         17.0   76      3
## 206 28.0         4         97.0         75   2155         16.4   76      3
## 207 26.5         4        140.0         72   2565         13.6   76      1
## 208 20.0         4        130.0        102   3150         15.7   76      2
## 209 13.0         8        318.0        150   3940         13.2   76      1
## 210 19.0         4        120.0         88   3270         21.9   76      2
## 211 19.0         6        156.0        108   2930         15.5   76      3
## 212 16.5         6        168.0        120   3820         16.7   76      2
## 213 16.5         8        350.0        180   4380         12.1   76      1
## 214 13.0         8        350.0        145   4055         12.0   76      1
## 215 13.0         8        302.0        130   3870         15.0   76      1
## 216 13.0         8        318.0        150   3755         14.0   76      1
## 217 31.5         4         98.0         68   2045         18.5   77      3
## 218 30.0         4        111.0         80   2155         14.8   77      1
## 219 36.0         4         79.0         58   1825         18.6   77      2
## 220 25.5         4        122.0         96   2300         15.5   77      1
## 221 33.5         4         85.0         70   1945         16.8   77      3
## 222 17.5         8        305.0        145   3880         12.5   77      1
## 223 17.0         8        260.0        110   4060         19.0   77      1
## 224 15.5         8        318.0        145   4140         13.7   77      1
## 225 15.0         8        302.0        130   4295         14.9   77      1
## 226 17.5         6        250.0        110   3520         16.4   77      1
## 227 20.5         6        231.0        105   3425         16.9   77      1
## 228 19.0         6        225.0        100   3630         17.7   77      1
## 229 18.5         6        250.0         98   3525         19.0   77      1
## 230 16.0         8        400.0        180   4220         11.1   77      1
## 231 15.5         8        350.0        170   4165         11.4   77      1
## 232 15.5         8        400.0        190   4325         12.2   77      1
## 233 16.0         8        351.0        149   4335         14.5   77      1
## 234 29.0         4         97.0         78   1940         14.5   77      2
## 235 24.5         4        151.0         88   2740         16.0   77      1
## 236 26.0         4         97.0         75   2265         18.2   77      3
## 237 25.5         4        140.0         89   2755         15.8   77      1
## 238 30.5         4         98.0         63   2051         17.0   77      1
## 239 33.5         4         98.0         83   2075         15.9   77      1
## 240 30.0         4         97.0         67   1985         16.4   77      3
## 241 30.5         4         97.0         78   2190         14.1   77      2
## 242 22.0         6        146.0         97   2815         14.5   77      3
## 243 21.5         4        121.0        110   2600         12.8   77      2
## 244 21.5         3         80.0        110   2720         13.5   77      3
## 245 43.1         4         90.0         48   1985         21.5   78      2
## 246 36.1         4         98.0         66   1800         14.4   78      1
## 247 32.8         4         78.0         52   1985         19.4   78      3
## 248 39.4         4         85.0         70   2070         18.6   78      3
## 249 36.1         4         91.0         60   1800         16.4   78      3
## 250 19.9         8        260.0        110   3365         15.5   78      1
## 251 19.4         8        318.0        140   3735         13.2   78      1
## 252 20.2         8        302.0        139   3570         12.8   78      1
## 253 19.2         6        231.0        105   3535         19.2   78      1
## 254 20.5         6        200.0         95   3155         18.2   78      1
## 255 20.2         6        200.0         85   2965         15.8   78      1
## 256 25.1         4        140.0         88   2720         15.4   78      1
## 257 20.5         6        225.0        100   3430         17.2   78      1
## 258 19.4         6        232.0         90   3210         17.2   78      1
## 259 20.6         6        231.0        105   3380         15.8   78      1
## 260 20.8         6        200.0         85   3070         16.7   78      1
## 261 18.6         6        225.0        110   3620         18.7   78      1
## 262 18.1         6        258.0        120   3410         15.1   78      1
## 263 19.2         8        305.0        145   3425         13.2   78      1
## 264 17.7         6        231.0        165   3445         13.4   78      1
## 265 18.1         8        302.0        139   3205         11.2   78      1
## 266 17.5         8        318.0        140   4080         13.7   78      1
## 267 30.0         4         98.0         68   2155         16.5   78      1
## 268 27.5         4        134.0         95   2560         14.2   78      3
## 269 27.2         4        119.0         97   2300         14.7   78      3
## 270 30.9         4        105.0         75   2230         14.5   78      1
## 271 21.1         4        134.0         95   2515         14.8   78      3
## 272 23.2         4        156.0        105   2745         16.7   78      1
## 273 23.8         4        151.0         85   2855         17.6   78      1
## 274 23.9         4        119.0         97   2405         14.9   78      3
## 275 20.3         5        131.0        103   2830         15.9   78      2
## 276 17.0         6        163.0        125   3140         13.6   78      2
## 277 21.6         4        121.0        115   2795         15.7   78      2
## 278 16.2         6        163.0        133   3410         15.8   78      2
## 279 31.5         4         89.0         71   1990         14.9   78      2
## 280 29.5         4         98.0         68   2135         16.6   78      3
## 281 21.5         6        231.0        115   3245         15.4   79      1
## 282 19.8         6        200.0         85   2990         18.2   79      1
## 283 22.3         4        140.0         88   2890         17.3   79      1
## 284 20.2         6        232.0         90   3265         18.2   79      1
## 285 20.6         6        225.0        110   3360         16.6   79      1
## 286 17.0         8        305.0        130   3840         15.4   79      1
## 287 17.6         8        302.0        129   3725         13.4   79      1
## 288 16.5         8        351.0        138   3955         13.2   79      1
## 289 18.2         8        318.0        135   3830         15.2   79      1
## 290 16.9         8        350.0        155   4360         14.9   79      1
## 291 15.5         8        351.0        142   4054         14.3   79      1
## 292 19.2         8        267.0        125   3605         15.0   79      1
## 293 18.5         8        360.0        150   3940         13.0   79      1
## 294 31.9         4         89.0         71   1925         14.0   79      2
## 295 34.1         4         86.0         65   1975         15.2   79      3
## 296 35.7         4         98.0         80   1915         14.4   79      1
## 297 27.4         4        121.0         80   2670         15.0   79      1
## 298 25.4         5        183.0         77   3530         20.1   79      2
## 299 23.0         8        350.0        125   3900         17.4   79      1
## 300 27.2         4        141.0         71   3190         24.8   79      2
## 301 23.9         8        260.0         90   3420         22.2   79      1
## 302 34.2         4        105.0         70   2200         13.2   79      1
## 303 34.5         4        105.0         70   2150         14.9   79      1
## 304 31.8         4         85.0         65   2020         19.2   79      3
## 305 37.3         4         91.0         69   2130         14.7   79      2
## 306 28.4         4        151.0         90   2670         16.0   79      1
## 307 28.8         6        173.0        115   2595         11.3   79      1
## 308 26.8         6        173.0        115   2700         12.9   79      1
## 309 33.5         4        151.0         90   2556         13.2   79      1
## 310 41.5         4         98.0         76   2144         14.7   80      2
## 311 38.1         4         89.0         60   1968         18.8   80      3
## 312 32.1         4         98.0         70   2120         15.5   80      1
## 313 37.2         4         86.0         65   2019         16.4   80      3
## 314 28.0         4        151.0         90   2678         16.5   80      1
## 315 26.4         4        140.0         88   2870         18.1   80      1
## 316 24.3         4        151.0         90   3003         20.1   80      1
## 317 19.1         6        225.0         90   3381         18.7   80      1
## 318 34.3         4         97.0         78   2188         15.8   80      2
## 319 29.8         4        134.0         90   2711         15.5   80      3
## 320 31.3         4        120.0         75   2542         17.5   80      3
## 321 37.0         4        119.0         92   2434         15.0   80      3
## 322 32.2         4        108.0         75   2265         15.2   80      3
## 323 46.6         4         86.0         65   2110         17.9   80      3
## 324 27.9         4        156.0        105   2800         14.4   80      1
## 325 40.8         4         85.0         65   2110         19.2   80      3
## 326 44.3         4         90.0         48   2085         21.7   80      2
## 327 43.4         4         90.0         48   2335         23.7   80      2
## 328 36.4         5        121.0         67   2950         19.9   80      2
## 329 30.0         4        146.0         67   3250         21.8   80      2
## 330 44.6         4         91.0         67   1850         13.8   80      3
## 332 33.8         4         97.0         67   2145         18.0   80      3
## 333 29.8         4         89.0         62   1845         15.3   80      2
## 334 32.7         6        168.0        132   2910         11.4   80      3
## 335 23.7         3         70.0        100   2420         12.5   80      3
## 336 35.0         4        122.0         88   2500         15.1   80      2
## 338 32.4         4        107.0         72   2290         17.0   80      3
## 339 27.2         4        135.0         84   2490         15.7   81      1
## 340 26.6         4        151.0         84   2635         16.4   81      1
## 341 25.8         4        156.0         92   2620         14.4   81      1
## 342 23.5         6        173.0        110   2725         12.6   81      1
## 343 30.0         4        135.0         84   2385         12.9   81      1
## 344 39.1         4         79.0         58   1755         16.9   81      3
## 345 39.0         4         86.0         64   1875         16.4   81      1
## 346 35.1         4         81.0         60   1760         16.1   81      3
## 347 32.3         4         97.0         67   2065         17.8   81      3
## 348 37.0         4         85.0         65   1975         19.4   81      3
## 349 37.7         4         89.0         62   2050         17.3   81      3
## 350 34.1         4         91.0         68   1985         16.0   81      3
## 351 34.7         4        105.0         63   2215         14.9   81      1
## 352 34.4         4         98.0         65   2045         16.2   81      1
## 353 29.9         4         98.0         65   2380         20.7   81      1
## 354 33.0         4        105.0         74   2190         14.2   81      2
## 356 33.7         4        107.0         75   2210         14.4   81      3
## 357 32.4         4        108.0         75   2350         16.8   81      3
## 358 32.9         4        119.0        100   2615         14.8   81      3
## 359 31.6         4        120.0         74   2635         18.3   81      3
## 360 28.1         4        141.0         80   3230         20.4   81      2
## 361 30.7         6        145.0         76   3160         19.6   81      2
## 362 25.4         6        168.0        116   2900         12.6   81      3
## 363 24.2         6        146.0        120   2930         13.8   81      3
## 364 22.4         6        231.0        110   3415         15.8   81      1
## 365 26.6         8        350.0        105   3725         19.0   81      1
## 366 20.2         6        200.0         88   3060         17.1   81      1
## 367 17.6         6        225.0         85   3465         16.6   81      1
## 368 28.0         4        112.0         88   2605         19.6   82      1
## 369 27.0         4        112.0         88   2640         18.6   82      1
## 370 34.0         4        112.0         88   2395         18.0   82      1
## 371 31.0         4        112.0         85   2575         16.2   82      1
## 372 29.0         4        135.0         84   2525         16.0   82      1
## 373 27.0         4        151.0         90   2735         18.0   82      1
## 374 24.0         4        140.0         92   2865         16.4   82      1
## 375 36.0         4        105.0         74   1980         15.3   82      2
## 376 37.0         4         91.0         68   2025         18.2   82      3
## 377 31.0         4         91.0         68   1970         17.6   82      3
## 378 38.0         4        105.0         63   2125         14.7   82      1
## 379 36.0         4         98.0         70   2125         17.3   82      1
## 380 36.0         4        120.0         88   2160         14.5   82      3
## 381 36.0         4        107.0         75   2205         14.5   82      3
## 382 34.0         4        108.0         70   2245         16.9   82      3
## 383 38.0         4         91.0         67   1965         15.0   82      3
## 384 32.0         4         91.0         67   1965         15.7   82      3
## 385 38.0         4         91.0         67   1995         16.2   82      3
## 386 25.0         6        181.0        110   2945         16.4   82      1
## 387 38.0         6        262.0         85   3015         17.0   82      1
## 388 26.0         4        156.0         92   2585         14.5   82      1
## 389 22.0         6        232.0        112   2835         14.7   82      1
## 390 32.0         4        144.0         96   2665         13.9   82      3
## 391 36.0         4        135.0         84   2370         13.0   82      1
## 392 27.0         4        151.0         90   2950         17.3   82      1
## 393 27.0         4        140.0         86   2790         15.6   82      1
## 394 44.0         4         97.0         52   2130         24.6   82      2
## 395 32.0         4        135.0         84   2295         11.6   82      1
## 396 28.0         4        120.0         79   2625         18.6   82      1
## 397 31.0         4        119.0         82   2720         19.4   82      1
cor(auto.without.name)
##                     mpg  cylinders displacement horsepower     weight
## mpg           1.0000000 -0.7776175   -0.8051269 -0.7784268 -0.8322442
## cylinders    -0.7776175  1.0000000    0.9508233  0.8429834  0.8975273
## displacement -0.8051269  0.9508233    1.0000000  0.8972570  0.9329944
## horsepower   -0.7784268  0.8429834    0.8972570  1.0000000  0.8645377
## weight       -0.8322442  0.8975273    0.9329944  0.8645377  1.0000000
## acceleration  0.4233285 -0.5046834   -0.5438005 -0.6891955 -0.4168392
## year          0.5805410 -0.3456474   -0.3698552 -0.4163615 -0.3091199
## origin        0.5652088 -0.5689316   -0.6145351 -0.4551715 -0.5850054
##              acceleration       year     origin
## mpg             0.4233285  0.5805410  0.5652088
## cylinders      -0.5046834 -0.3456474 -0.5689316
## displacement   -0.5438005 -0.3698552 -0.6145351
## horsepower     -0.6891955 -0.4163615 -0.4551715
## weight         -0.4168392 -0.3091199 -0.5850054
## acceleration    1.0000000  0.2903161  0.2127458
## year            0.2903161  1.0000000  0.1815277
## origin          0.2127458  0.1815277  1.0000000
#as.data.frame(as.table(cor(auto.without.name)))
lm.fit.auto.mul = lm(mpg ~ ., data = auto.without.name)
summary(lm.fit.auto.mul)
## 
## Call:
## lm(formula = mpg ~ ., data = auto.without.name)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.5903 -2.1565 -0.1169  1.8690 13.0604 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -17.218435   4.644294  -3.707  0.00024 ***
## cylinders     -0.493376   0.323282  -1.526  0.12780    
## displacement   0.019896   0.007515   2.647  0.00844 ** 
## horsepower    -0.016951   0.013787  -1.230  0.21963    
## weight        -0.006474   0.000652  -9.929  < 2e-16 ***
## acceleration   0.080576   0.098845   0.815  0.41548    
## year           0.750773   0.050973  14.729  < 2e-16 ***
## origin         1.426141   0.278136   5.127 4.67e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.328 on 384 degrees of freedom
## Multiple R-squared:  0.8215, Adjusted R-squared:  0.8182 
## F-statistic: 252.4 on 7 and 384 DF,  p-value: < 2.2e-16
plot(lm.fit.auto.mul)

lm.fit.auto.mul1 = lm(mpg ~ displacement*cylinders + displacement * weight, data = auto.without.name)
summary(lm.fit.auto.mul1)
## 
## Call:
## lm(formula = mpg ~ displacement * cylinders + displacement * 
##     weight, data = auto.without.name)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.2934  -2.5184  -0.3476   1.8399  17.7723 
## 
## Coefficients:
##                          Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             5.262e+01  2.237e+00  23.519  < 2e-16 ***
## displacement           -7.351e-02  1.669e-02  -4.403 1.38e-05 ***
## cylinders               7.606e-01  7.669e-01   0.992    0.322    
## weight                 -9.888e-03  1.329e-03  -7.438 6.69e-13 ***
## displacement:cylinders -2.986e-03  3.426e-03  -0.872    0.384    
## displacement:weight     2.128e-05  5.002e-06   4.254 2.64e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.103 on 386 degrees of freedom
## Multiple R-squared:  0.7272, Adjusted R-squared:  0.7237 
## F-statistic: 205.8 on 5 and 386 DF,  p-value: < 2.2e-16
plot(lm.fit.auto.mul1)

From the above result, we can see that cylinders and the interaction displacement*cylinders are not significant.

lm.fit.auto.mul2 = lm(mpg ~ displacement + weight + displacement:weight, data = auto.without.name)
summary(lm.fit.auto.mul2)
## 
## Call:
## lm(formula = mpg ~ displacement + weight + displacement:weight, 
##     data = auto.without.name)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.8664  -2.4801  -0.3355   1.8071  17.9429 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          5.372e+01  1.940e+00  27.697  < 2e-16 ***
## displacement        -7.831e-02  1.131e-02  -6.922 1.85e-11 ***
## weight              -8.931e-03  8.474e-04 -10.539  < 2e-16 ***
## displacement:weight  1.744e-05  2.789e-06   6.253 1.06e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.097 on 388 degrees of freedom
## Multiple R-squared:  0.7265, Adjusted R-squared:  0.7244 
## F-statistic: 343.6 on 3 and 388 DF,  p-value: < 2.2e-16
plot(lm.fit.auto.mul2)